The pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.
What is Simple interest?Borrowers are required to pay the lender's basic interest as a fee in exchange for a loan.
Compound interest is not taken into account in the calculation; just the initial principal is taken into account.
Simple interest applies to all loans, not just specific ones.
Also highlighted is the type of interest that banks provide their customers on their savings accounts.
So, we presumptively have $x invested in the savings account.
Consequently, $ was invested in the development plan.(6150 - x).
S.I. = (Prt)/100 is the formula for simple interest on a sum of money (P), compounded at a rate (r), over a time period (t).
We figure out the interest on both investments:
Contribution to a savings account:
Amount invested (P) = $x.
Rate of interest (r) = 6%.
Time for investment (t) = 1 year.
As a result, interest was received= (Prt)/100 = $(x*6*1)/100 = $ (6x)/100
We are aware that $477 in interest has been paid in total.
Thus, we can write the following equation using the interest from both investments added:
(6x)/100 + {9(6150 - x)}/100 = 477
or, 6x + 55350 - 9x = 47700,
or, 55350 - 47700 = 3x,
or, 3x = 7650,
or x = 7650/3 = 2550.
As a result, investments in:
Savings account = $x = $2550.
Development plan = $(6150 - x) = $(6150 - 2550) = $3600.
Therefore, the pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.
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Correct question:
In investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477. How much money was invested at each rate?
What is the side length
Check the picture below.
a) Find the mean and median of the following gasoline prices per gallon in California:
regular:
$
3.14
$3.14, mid-grade:
$
3.21
$3.21, premium:
$
3.28
$3.28, diesel:
$
3.53
$3.53. Round to the nearest cent.
The mean and the median of the following gasoline prices that are listed above would be =3.29 and 4.85 respectively.
How to calculate the mean and median of a data set?The formula that is used to calculate the mean of a data set is given as follows;
mean = sum of data set/number of data set
= 3.14+3.21+3.28+3.53/4
= 13.16/4 = 3.29
The median = 3.21+3.28/2 = 4.85
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Quiz Active
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Which dimensions can create more than one triangle?
three angles measuring 25°, 65°, and 90°
three angles measuring 50°, 50°, and 50°
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8 ft, and 10 ft
10
The dimensions that can create more than one triangle are given as follows:
three angles measuring 25°, 65°, and 90°.
What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The sum of the measures of the internal angles of a triangle is of:
180º.
Meaning that the first option is correct and the second is not.
Considering the law of sines, an infinite number of triangles can be formed, as long as:
sin(25º)/a = sin(65º)/b = sin(90º)/c.
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What’s the current yield of a 4.95 percent coupon corporate bond quoted at a price of 102.53?
The current yield of a 4.95% coupon at a price of $102.53 is [tex]4.82%[/tex]%.
What is the current yield of a 4.95% coupon bond?The current yield of bond means return on an investment based on its current market price.
To calculate the current yield, we will use (annual interest payment/current market price * 100).
Annual interest payment = $1,000 face value x 4.95% coupon
Annual interest payment = $49.50
Current market price = 102.53% of the face value
Current market price = $1,025.30
Current yield = $49.50 / $1,025.30 x 100
Current yield = 4.82%
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Which of the following points is in the solution set of y < x^2 - 2x - 8?
The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)
What is the solution about?When you Check the inequality by (-2,-1) then Put x=-2 and y=-1 in the given inequality.
1 < (-2)² - 2(-2) - 8
-1 < 4 + 4 - 8
-1 < 0
Hence:
(-2,-1) can be in the solution
( 0,-2) Cannot
(4,0) will not.
Therefore, The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)
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See full question below
Which of the following points is in the solution set of y < x2 - 2x - 8?
(-2, -1)(0, -2)(4, 0)
34°
ength of b
3
C
10
First, complete the equation.
c²= a² + b² - 2abcosC
c²=32 10²-2(3)([?]) cos
Enter the side length that belongs in the green box.
Enter
The complete equation for the cosine rule is c² = 3² + 10² - 2(3)(10) × cos(34).
What is cosine rule?The cosine rule, also known as the law of cosines, is a formula used to find the lengths of sides or measures of angles in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. The cosine rule is typically used when you have a triangle with at least one known side length and its opposite angle, and you want to find either another side length or another angle in the triangle.
The cosine rule is given by the following formula:
c² = a² + b² - 2ab × cos(C)
where:
c is the length of the side opposite to angle Ca and b are the lengths of the other two sidesC is the measure of the angle opposite to side ccos(C) is the cosine of angle CFor the given side c;
c² = 3² + 10² - 2(3)(10) × cos(34)
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I need help on this
Answer:
1.5=slope
Step-by-step explanation:
To do this, we need to solve the slope.
We will use rise/run
0-3=-3
0-2=-2
-3/-2=1.5
Please help
Question in image
Answer:
55.5
Step-by-step explanation:
Using the Tangent and Intersected Chord Theorem we know that since the line is tangent to the circle, it will be half of the arc that surrounds the angle. Becuase the arc is 111, dividing it by 2 will give us 55.5
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. If the container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
The total weight of the contents is 141.33 pounds.
What is a rectangular prism?
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
Here, we have
Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.
The volume of the container is calculated as:
5 ft× 14.5 ft× 6.5 ft= 471.125 ft³
Then, the total weight of the contents is calculated as:
471.125 ft³× 0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds
Hence, the total weight of the contents is 141.33 pounds.
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Cassie uses 1 quart cranberry juice, 1/2 gallon ginger ale, and 1 1/2 pint orange juice to make friut punch .How many 6- ounce servings can she make
She can make 20 6-ounce servings to make fruit punch
How to determine this
Cassie uses 1 quart cranberry juice,
1/2 gallon ginger ale,
1 1/2 pint orange juice.
1 quart of cranberry juice when converted to ounce
1 quart = 32 ounces
1/2 gallon of ginger ale when converted to ounce
1 gallon = 128 ounces
1/2 gallon = 128/2
1/2 gallon = 64 ounces
1 1/2 pint orange juice to make fruit punch
1 pint = 16 ounces
1 1/2 pint = 16 + 16/2 ounces
= 16 + 8
= 24 ounces
How many 6-ounces servings can she make
32 + 64 + 24
= 120 ounces
6-ounces that can be made
= 120 ounces/6 ounces
= 20 servings
Therefore, 20 6-ounce servings can be make for fruit punch
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PLS HELP ASAP!!!
A triangle is shown in the image. A triangle with a height of 12 inches. The height is perpendicular to the base labeled 36 inches. The side from the top of the perpendicular side to the base is labeled 34 inches. What is the area of the triangle represented? 204 in2
216 in2
408 in2
432 in2
So the area of the triangle is 216 square inches.
How is area of a triangle determined?To find the area of a triangle, you can use the formula A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle. In this case, we have a height of 12 inches and a base of 36 inches.
To find the length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, we have:
c² = a² + b²
c² = 12² + 34²
c² = 144 + 1156
c² = 1300
c = √(1300)
c = 36.06 (rounded to two decimal places)
Now that we know all three sides of the triangle, we can plug them into the formula for the area:
A = 1/2 * b * h
A = 1/2 * 36 * 12
A = 216
So the area of the triangle is 216 square inches.
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An arrow is launched upward with a velocity of 256
feet per second from the top of a 80
-foot stage. What is the maximum height attained by the arrow?
The maximum height attained by the arrow is 2128 feet
What is kinematic equation for vertical motion?
The kinematic equation for vertical motion is [tex]h = h_0 + v_0 \times (\frac{1}{2} )t - gt^2[/tex]
where:
h = height attained by the arrow (maximum height)
[tex]h_0 = [/tex]initial height (80 feet)
[tex]v_0 = [/tex]initial velocity (256 feet per second)
g = acceleration due to gravity (-32 feet per second squared)
t = time taken to reach maximum height
At the maximum height, the velocity of the arrow is zero. So we can use the fact that the final velocity is zero to find the time taken to reach the maximum height,
[tex]0 = v_0 - g \times t \\ t = \frac{ v_0}{g}[/tex]
Substituting this value of t into the first equation, we get:
[tex]h = h_0 + v_0 \times ( \frac{v_0}{g}) - ( \frac{1}{2} )g( \frac{v_0}{g})^2 \\ h = 80 + (256) \frac{256}{(-32)} - ( \frac{1}{2} )(-32)\frac{256^2}{(-32)^2} \\ h = 80 + 4096 - ( \frac{1}{2} ) \frac{(256)^2}{(32)} \\ h = 80 + 4096 - 2048 \\ h = 2128 \: feet[/tex]
Therefore, the maximum height attained by the arrow is 2128 feet.
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Which functions have a y-intercept that is greater than the y-intercept of the function g(x)=x+31 +4? Check three
options.
f(x)=-2 (x-8)²
Oh(x) = -5 1x1 + 10
(x)=-4(x + 2)² +8
K(x)=(x-4)²+4
m(x)=x-81+6
The functions which have a y-intercept which is greater than the y-intercept of the function g(x) = |x + 3| + 4 are :
h(x) = -5 |x| + 10
k(x) = 1/4 (x - 4)² + 4
m(x) = 1/4 |x - 8| + 6
Given function is,
g(x) = |x + 3| + 4
y intercept of a function is the value of the function when the input value is 0.
g(0) = |0 + 3| + 4 = 7
f(x) = -2 (x - 8)²
f(0) = -2 (0 - 8)² = -128
h(x) = -5 |x| + 10
h(0) = 10
j(x) = -4(x + 2)² + 8
j(0) = -4 (0 + 2)² + 8 = -8
k(x) = 1/4 (x - 4)² + 4
k(0) = 1/4 (0 - 4)² + 4 = 8
m(x) = 1/4 |x - 8| + 6
m(0) = 1/4 |0 - 8| + 6 = 8
Hence the functions h(x) = -5 |x| + 10, k(x) = 1/4 (x - 4)² + 4 and m(x) = 1/4 |x - 8| + 6 have the y intercept greater than that of g(x) = |x + 3| + 4.
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Give a recursive definition for the following set of ordered pairs of positive integers ([tex]a|b[/tex] means that a is a factor of b): [tex]S=[/tex]{[tex](a,b)|a \in Z^+, b \in Z^+, a|b[/tex]}
A recursive definition for the set S can be given as follows:
What is recursion?
Recursion is a programming technique where a function calls itself to solve a problem.
Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.
Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.
In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.
The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.
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ctaivity 1: how do you see it? state whether or not the following triangles are similar if not ,explain why not .if so,write a similarity statement
Triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.
What are similar triangles?Two triangles that are similar in shape but not necessarily in size are called similar triangles. To put it another way, the two triangles' angles are similar and their corresponding sides are proportional.
If two triangles are comparable, then all pairs of related sides have the same length-to-length ratio. The scale factor of similar triangles is the name given to this ratio. The scale factor between two triangles is 2:1, for instance, if one side of a triangle is twice as long as its counterpart side in another triangle.
In the given figure we have triangle RLG and triangle PCN.
Here, the ratio of the sides of the triangle are given as:
RG / PN = 32 / 48 = 2/3
Also we have:
LG / PC = 18/27 = 2/3
LR / CN = 30 / 45 = 2/3
RG / PN = LG / PC = LR / CN = 2/3
Hence, triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.
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The complete question is:
In a study relating to the labourers of a jute mill in West Bengal, the following information was collected. ‘Twenty per cent of the total employees were females and forty per cent of them were married. Thirty female workers were not members of Trade Union. Compared to this, out of 600 male workers 500 were members 11 of Trade Union and fifty per cent of the male workers were married. The unmarried non-member male employees were 60 which formed ten per cent of the total male employees. The unmarried non-members of the employees were 80’. On the basis of this information, the ratio of married male non-members to the married female non-members is (a) 1 : 3 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1
On the basis of this information, the ratio of married male non-members to the married female non-members is (b) 3 : 1
How to calculate the ratioTotal married male employees = 80% × 50% = 40%
Total male Trade Union members = 91.67%
Total male non-Trade Union members = 100% - 91.67% = 8.33%
Married male Trade Union members = 40% × 91.67% = 36.67%
Married male non-Trade Union members = 40% - 36.67% = 3.33%
Now, let's find the number of married female non-members:
The ratio based on the information is 3 to 1.
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when the dimensions of a two-dimensional shape are doubled then what is the perimeter
The figure below shows roads near a pond. Each segment of the triangle represents a road or a path, except AB which represents the distance across the pond. Are the two triangles similar?
Answer:
Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.
At a college financial aid office, students who applied for a scholarship were classified according to their class rank: Fr = freshman, So = sophomore, Jr = junior, Se = senior. Construct a frequency distribution for the data.
Fr Fr So Jr Se
Se Fr Jr Fr Fr
Fr Fr So So Fr
Jr Se Se Se Jr
Jr So Fr So Jr
Fr So Jr Se Se
Answer:
Class Rank | Frequency
--- | ---
Fr | 7
So | 3
Jr | 4
Se | 6
Construct an Argument | Batter is being poured into the right rectangular prism-shaped pan so that the pan is full. What is the volume of the batter in the pan? 9 in. 3 In. 5 in.
Answer:
Valid
Step-by-step explanation:
The volume of the batter in the pan can be found by multiplying the length, width, and height of the right rectangular prism-shaped pan. In this case, the length is 9 inches, the width is 5 inches, and the height is 3 inches.
Using the formula for the volume of a rectangular prism, V = lwh, we can substitute the given values to find:
V = (9 in.)(5 in.)(3 in.)
V = 135 cubic inches
Therefore, the volume of the batter in the pan is 135 cubic inches. This argument is valid because it follows the basic formula for calculating the volume of a rectangular prism and uses the specific measurements provided for the length, width, and height of the pan.
please answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
(a) Lena got 33 more
(b) Last one
what is the length of a scaled drawing with a width of 9cm and the scale factor 3/4?
The length of a scaled drawing with a width of 9cm and the scale factor 3/4 s 6.75 cm
Calculating the length of a scaled drawingFrom the question, we have the following parameters that can be used in our computation:
Width = 9cm
Scale factor = 3/4
Using the above as a guide, we have the following:
Length of a scaled drawing = Width * Scale factor
Substitute the known values in the above equation, so, we have the following representation
Length of a scaled drawing = 9 * 3/4
Evaluate
Length of a scaled drawing = 6.75
Hence, the length of a scaled drawing is 6.75 cm
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Question 1(Multiple Choice Worth 2 points)
(Slope-Intercept Form MC)
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
Question 2(Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.
Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?
2.5 weeks
5 weeks
15 weeks
75 weeks
Question 3(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Polygon ABCD is rotated to get polygon A′B′C′D′.
Graph of polygon ABCD in quadrant 2 with point A at negative 7 comma 5, point B at negative 2 comma 8, point C at negative 2 comma 4, and point D at negative 4 comma 3 and polygon A prime B prime C prime D prime in quadrant 1 with point A prime at 5 comma 7, point B prime at 8 comma 2, point C prime at 4 comma 2, and point D prime at 3 comma 4
Determine the direction and angle of rotation.
270° clockwise rotation
270° counterclockwise rotation
90° counterclockwise rotation
180° clockwise rotation
Question 4(Multiple Choice Worth 2 points)
(Scatter Plots MC)
Data was collected on the price per cupcake on orders of different amounts from a bakery. The scatter plot shows the data that was gathered.
scatter plot titled cupcake pricing with the x axis labeled number of cupcakes and the y axis labeled cost per cupcake in dollars with points at 1 comma 6, 2 comma 5, 2 comma 5.5, 3 comma 5.5, 4 comma 5, 4 comma 5.5, 5 comma 4.5, 6 comma 3.5, 7 comma 2, 8 comma 1, and 9 comma 0.5
Which of the following describes the pattern of association for the scatter plot?
There is a weak, positive linear association.
There is a weak, negative linear association.
There is a strong, positive nonlinear association.
There is a strong, negative nonlinear association.
Question 5(Multiple Choice Worth 2 points)
(Similar Triangles MC)
Triangle ABC ~ triangle DEF.
triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Determine the measurement of FD.
FD = 1.52
FD = 1.58
FD = 1.1
FD = 5.5
Question 6(Multiple Choice Worth 2 points)
(Slope MC)
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
Question 7(Multiple Choice Worth 2 points)
(Experimental Probability MC)
An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
Question 8(Multiple Choice Worth 2 points)
(Dilations MC)
Triangle ABC is dilated to produce triangle A′B′C′.
Graph of a triangle ABC with vertices at A 10 comma 2, B 18 comma 2, C 18 comma 10. Triangle A prime B prime C prime with vertices at A prime 5 comma 1, B prime 9 comma 1, C prime 9 comma 5.
Determine the scale factor used to create the image.
one fourth
one half
2
4
The slope of the line is -4, which means that the swimmer will complete 4 laps every minute. For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).
The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.
To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x
10x + 25 = 5x + 50
5x = 25
x = 5
So, after 5 weeks, the two siblings will have the same amount of money saved.
The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.
The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.
Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles
AB/DE = BC/EF = CA/FD
Plugging in the known values, we get
11/2.2 = 7.9/EF = 7.6/FD
Solving for FD, we get
FD = (7.6 * 2.2)/11 = 1.52
So, FD has a length of 1.52 units.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula
slope = (y2 - y1)/(x2 - x1)
Plugging in the given values, we get
slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2
So, the slope of the line is negative three halves.
The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials
P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%
So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.
Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.
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Let v be the vector from initial point P₁ to terminal point P2. Write v in terms of i and j.
P₁ = (-5,3), P2=(-2,-7)
V=
(Type your answer in terms of i and j.)
By subtraction between two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7), the vector V is 3 i - 10 j.
How to determine the vector
According to linear algebra, a vector can be formed by subtracting the initial point (P₁) from the final point (P₂). The equation is introduced below:
V = P₂(x, y) - P₁(x, y)
V = (- 2, - 7) - (- 5, 3)
V = (3, - 10)
V = 3 i - 10 j
The vector V = 3 i - 10 j is the result of subtracting the two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7).
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Posted a image so that you can see it
The missing values are b = 4.37, C = 11° and A = 134°
Given is a triangle, we need to find the missing lengths and angles,
So,
Using the cosine rule,
b² = a²+c² - 2ac Cosb
b = √4²+7²-2(4)(7)cos35°
b = √16+49-45.87
b = √19.13
b = 4.37
Now, using the sine rule,
Sin C / 7 = Sin 35° / 4.37
C = 11°
Applying the angle sum property of triangles,
A = 180°-(11°+35°)
A = 134°
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Can someone help me with this problem?
Answer:
∠ BAC = 66°
Step-by-step explanation:
the inscribed angle BAC is half the angle at the centre, subtended on the same arc BC , then
∠ BAC = [tex]\frac{1}{2}[/tex] × 132° = 66°
Directions: Read the scenario below and solve. Show your
work.
If given x > 0 and y> 0, in which quadrant or axis will each
ordered pair described below lie? Explain your answer.
a. (-x, y)
b. (-x, 0)
c. (x, -y)
d. (0. y)
The quadrant or axis for each of the given ordered pairs is:
a. (-x, y) - second quadrant
b. (-x, 0) - X-axis
c. (x, -y) - fourth quadrant
d. (0, y) - Y-axis
How to determine the quadrantsa. (-x, y):
As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.
b. (-x, 0):
The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.
c. (x, -y):
The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.
d. (0, y):
In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.
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Point P is on the terminal side of angle theta.
Find cot of theta.
Point P is located at (0, 5)
Check the picture below, so the angle looks more or less like so.
now, let's recall that the value pair in a terminal point is the adjacent and opposite sides
[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{0}}{\underset{opposite}{5}}\implies \cot(\theta )=0[/tex]
Based only on the information given in
theorems or postulates could be given as reasons why AHIJKLM?
Check all that apply.
H
A. LL
L
a
K
B. AAS
C. ASA
D. LA
☐E. HA
OF. HL
MA
The congruency rules which satisfy the given triangles are (B) AAS and (D) HA.
What is triangle congruency?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
If two triangles meet all 5 requirements for congruence, then they are congruent.
They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS). (RHS).
So, according to the given, we can observe that:
2 pairs of angles are congruent one pair of which is 90°.
And 1 pair of sides are congruent.
Then, the rules that satisfy here will be:
AAS and HA
Therefore, the congruency rules which satisfy the given triangles are (B) AAS and (D) HA.
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Complete question:
Based only on the information given in the diagram, which congruence theorems or postulates could begin as reasons why HIJ = KLM?
Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope of the line that is parallel to the line that contains side WV?
-2
2
-1
1
The slope of the line that is parallel to the line that contains side WV is 1.
What about slope of line?
The slope of a line is a measure of its steepness or inclination, defined as the ratio of the change in the vertical direction (y-axis) to the change in the horizontal direction (x-axis) between any two points on the line.
In other words, the slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is commonly denoted by the letter "m" and is calculated as:
m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line rises as we move from left to right, while a negative slope indicates that the line falls as we move from left to right. A slope of zero indicates that the line is horizontal, and an undefined slope indicates that the line is vertical.
According to the given information:
W(a+3, b-3) and V(a+5, b-1)
So, the slope WV,
[tex]\frac{b-3-(b-1)}{a+3 - (a+5)} \\\\\frac{-2}{-2} = 1[/tex]
So, the slope of the given condition is 1.
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